Multiplicity of Normalized Solutions for Schrodinger Equations

In this paper, we consider the following nonlinear Schr & ouml;dinger equation with an L-2 -constraint: { -Delta u=lambda u+mu|u|(q-2)u+|u|(p-2)u in R-N, integral(N)(R)|u|(2)dx=a(2),u is an element of H-1(R-N) where N >= 3,a,mu >0, 2<q<2+4/N<p<2(& lowast;),2q+2N-pN<0 and lambda is an element of R arises as a Lagrange multiplier. We deal with the concave and convex cases of energy functional constraints on theL2sphere, and prove the existence of infinitely solutions with positive energy levels.